When can t terminal pairs in an m × n grid be connected by t vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch's 1975 proof without the “cover all vertices” constraint, and Kotsuma and Takenaga's 2010 proof when the paths are restricted to have the fewest possible corners within their homotopy class. The latter restriction is a common form of the famous Nikoli puzzle Numberlink. Our problem is another common form of Numberlink, sometimes called Zig-Zag Numberlink and popularized by the smartphone app Flow Free.
A parallelohedron is a convex polyhedron which fills the space by translations only. There are five families of parallelohedra. A pentadron is a pentahedron whose copies compose at least one member of every family of parallelohedra. A pentadral complex is a convex polyhedron which is constructed by combining copies of pentadra in a face-to-face gluing manner. In this paper, reversibilities and tessellabilities of pentadral complices and their related topics are studied.
The anti-slide packing is a packing of a number of three dimensional pieces of same size into a larger box such that none of them can slide in any direction. In this paper, we consider the problem of how to find a sparsest anti-slide packing. We give an IP formulation of this problem, and obtain the solutions for some small cases by using an IP solver. In addition, we give the upper and lower bounds on the ratio of the volume occupied by the pieces when the size of a box approaches infinity. For the case of piece size 2 × 2 × 1, we show that a sparsest anti-slide packing occupies at least 28.8% and at most 66.7% of the total volume.
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each slot, we multiply the slot index with the number in this slot, and add up the products. The goal of the game is to maximize this score. In more detail, we play the game many times, and try to maximize the sum of scores or, equivalently, the expected score. We present a strategy to optimally play this game with respect to the expected score. We then modify our strategy so that we need only polynomial time and space. Finally, we show that knowing all ten rolls in advance, results in a relatively small increase in score. Although the game has a random component and requires a non-trivial strategy to be solved optimally, this strategy needs only polynomial time and space.
This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.
We propose a class of chess variants, Multimove Chess (i, j), in which White gets i moves per turn and Black gets j moves per turn. One side is said to win when it takes the opponent's king. All other rules of chess apply. We prove that if (i, j) is not (1, 1) or (2, 2), and if i ≥ min(j, 4), then White always has a winning strategy, and if i < min(j, 4), Black always has a winning strategy.
Among many variations of pencil puzzles, Latin square Completion-Type puzzles (LSCPs) are quite popular for puzzle fans. Concerning these puzzles, the solvability has been investigated from the viewpoint of time complexity in the last decade; it has been shown that, in most of these puzzles, it is NP-complete to determine whether a given puzzle instance has a proper solution. In this paper, we investigate the approximability of three LSCPs: Sudoku, Futoshiki and Kenken. We formulate each LSCP as a maximization problem that asks to fill as many cells as possible, under the Latin square condition and the inherent condition. We then propose simple generic approximation algorithms for them and analyze their approximation ratios.
In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.
Ghost is a popular word game played by two or more players. Players take turns adding a letter to the end of a growing word fragment, trying not to be the first to complete a valid word. We show that the game, when played on a regular language, is PSPACE-hard, and extend the result to four variants of the game. In addition, we take advantage of a quirk of the German language — that German words can be concatenated together to form longer words — to give a fun extension of our proof of PSPACE-hardness to subsets of the German language.
This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness and truthfulness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed approximately but asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n-1 where n is the number of players, which is the minimum. Sgall and Woeginger proposed another asynchronous protocol that satisfies simple fairness, truthfulness, and the minimum number of cuts. These two protocols are compared from the viewpoint of social surplus. The simulation result shows that the cryptographic moving-knife protocol is better than the Sgall-Woeginger protocol.
Three-point tiling is the problem to cover all the lattice points in a triangular region of the triangular lattice with triangle tiles that connect three adjacent lattice points. All the lattice points must be used by exactly one triangle tile. In this paper, we enumerate all the solutions and rotation symmetric solutions using ordered binary decision diagrams. In addition, the number of essentially different solutions, any two of which do not become identical by rotating and turning over, is computed.
We study the computational complexity of a packing puzzle Fillmat, which is a type of pencil-and-paper puzzles made by Japanese puzzle publisher Nikoli. We show that the problem to decide if a given instance of Fillmat has a solution is NP-complete by a reduction from the circuit-satisfiability problem (Circuit-SAT). Our reduction is carefully designed so that we can also prove ASP-completeness of the another-solution-problem.
In the field of systems development, linking models are expected for each process to improve understandability and productivity. For example, when Soft Systems Methodology is applied to the uppermost process in a stream and an Object-Oriented Approach is applied to the upstream and midstream processes, if the conceptual activity model of the former and the class diagram of the latter can be linked, then we can build systems that are intuitively simple to understand, easily maintained, and reusable. This paper considers a system's root definition and proposes an approach for spatial arrangement through multidimensional scaling of responsibilities extracted from a conceptual activity model. We tested our proposed approach on several samples and obtained a spatial responsibility arrangement that is quite reasonable. We believe this approach has the potential to bridge artifacts from the uppermost stream, including conceptual activity models and midstream artifacts represented by class diagrams.
In Twitter and other microblogging services, users often have large social networks formed around cliques (communities) such as friends, coworkers or former classmates. However, the membership of each user in multiple cliques makes it difficult to process information and interact with other clique members. We address this problem by automatically dividing the social network of a Twitter user into personal cliques and assigning keywords to each clique to identify the common ground of its members. In this way, the user can understand the structure of their social network and interact with the members of each clique independently. Our proposed method improves clique annotation by not only extracting keywords from the tweet history of the clique members, but individually weighting the extracted keywords of each member according to the relevance of their tweets for the clique. The keyword weight is influenced by two factors. The first factor is calculated based on the number of connections of a user within the clique, and the second factor depends on whether the user publishes personal information or information of general interest. We developed the prototype of a Twitter client with clique management functionality and conducted an experiment in which on average 46.96% of the keywords extracted from our proposed method were relevant for the cliques as opposed to 38.31% for the baseline method.
The increased popularity of mobile devices, such as laptops, mobile phones, tablets, accessory devices, and more, brings new challenges in the area of network security in the ubiquitous environment, where ad-hoc networks may be formed using mobile devices. There has been little discussion of setting up secure connections among a group of devices. A number of group security protocols has been proposed; however, these have tended to focus on a scenario whereby all devices must be located in one place at one time. In this paper, we describe a new secure group association method that associates mobile devices in an accumulative manner, so it does not require all group members to be physically present. It utilizes digital certification and extends the concept of out-of-band channels, through which the authentication data can be transferred using human user involvement. We have implemented a prototype system and conducted a comparative user experiment to demonstrate viability of the accumulative association.
Over the last decade, an increasing amount of work has been done to advance the phrase-based statistical machine translation model in which the method of extracting phrase pairs consists of word alignment and phrase extraction. In this paper, we show that, for Japanese-English and Chinese-English statistical machine translation systems, this method is indeed missing potentially useful phrase pairs which could lead to better translation scores. These potentially useful phrase pairs can be detected by looking at the segmentation traces after decoding. We choose to see the problem of extracting potentially useful phrase pairs as a two-class classification problem: among all the possible phrase pairs, distinguish the useful ones from the not-useful ones. As for any classification problem, the question is to discover the relevant features which contribute the most. Extracting potentially useful phrase pairs resulted in a statistically significant improvement of 7.65 BLEU points in English-Chinese and 7.61 BLEU points in Chinese-English experiments. A slight increase of 0.94 BLEU points and 0.4 BLEU points is also observed for English-Japanese system and Japanese-English system, respectively.
Recently, the sizes of XML documents have rapidly been increasing. Distributed XML is a novel form of XML document, in which an XML document is partitioned into fragments and managed separately in plural sites. Distributed XML documents can often be managed more easily than a single large document, according to geographical and/or administrative factors. In this paper, we consider performing XSLT transformation efficiently for distributed XML. To obtain an efficient method for this transformation, we devise an efficient evaluation method for XSLT pattern, which is a subset of XPath, and integrate it into top-down XSLT transformation. To evaluate an XSLT pattern for node v in a distributed environment, the site having v may need to access other sites many times. We propose two novel techniques to reduce such accesses; (1) precomputation of ancestors and (2) cache for predicate evaluation. We implemented our method in Ruby and made evaluation experiments. This result suggests that our method is more efficient than a centralized approach.
We propose an improved method for hierarchical-matrices (H-matrices) using adaptive cross approximation (ACA) as the low-rank approximation. The improvement consists of a kind of normalization and a new stopping criterion for the ACA. By using the proposed method, we can avoid the trouble that ranks of approximated matrices increase rapidly as the matrix size increases when the conventional H-matrices with ACA are employed to an integral equation whose kernel function has high-order singularities. In particular, application of the proposed method enables us to perform large-scale simulations such that the conventional H-matrices with ACA fail to construct the low-rank approximation. Applicability of the proposed method is confirmed through numerical experiments on an earthquake cycle simulation.
In the world of digital photography, it is widely known that general contexts including location, date, time, weather condition, composition, and camera setting, obviously affect quality of photos. In this paper, we analyzed the crowdsourced big data on the social network for photographers and extracted the rich photographic information in order to assist photographers to take beautiful photos. Our developed system is composed of server-side system and mobile application. The server-side system suggests good photos which are relevant to the contexts. The sophisticated iOS application was developed to collect the contexts and exhibit the result. The user's satisfaction in Phorec were measured through subjective evaluations. The result reflected that recommended photography settings are important and can fulfil user's desire.